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The control properties of discrete-time switched linear systems (SLS) with switching signals generated by logical dynamic systems are studied using the semi-tensor product (STP) approach. With the algebraic state space representation…
The increasing integration of renewable energy sources has introduced complex dynamic behavior in power systems that challenge the adequacy of traditional continuous-time modeling approaches. These developments call for modeling frameworks…
We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with…
Formal Laurent-Puiseux series are important in many branches of mathematics. This paper presents a {\it Mathematica} implementation of algorithms developed by the author for converting between certain classes of functions and their…
In this work, we present a logical formalism for reasoning about quantum systems in finite dimension. Contrary to the usual approach in quantum logic, our formalism is based classical first-order logic, which allows us to use the tools of…
We present a procedure for reducing the number of continuous states of discrete-time linear switched systems, such that the reduced system has the same behavior as the original system for a subset of switching sequences. The proposed method…
The design of decision and control strategies for switched systems typically requires complete knowledge of (i) mathematical models of the subsystems and (ii) restrictions on admissible switches between the subsystems. We propose an active…
We study the notion of structured realizability for linear systems defined over graphs. A stabilizable and detectable realization is structured if the state-space matrices inherit the sparsity pattern of the adjacency matrix of the…
Conventional finite-difference schemes for solving partial differential equations are based on approximating derivatives by finite-differences. In this work, an alternative theory is proposed which view finite-difference schemes as…
Randomized quantum algorithms have been proposed in the context of quantum simulation and quantum linear algebra with the goal of constructing shallower circuits than methods based on block encodings. While the algorithmic complexities of…
The current verification flow of complex systems uses different engines synergistically: virtual prototyping, formal verification, simulation, emulation and FPGA prototyping. However, none is able to verify a complete architecture.…
This paper establishes that generic linear quantum stochastic systems have a pure cascade realization of their transfer function, generalizing an earlier result established only for the special class of completely passive linear quantum…
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
This paper presents a four-stage algorithm for the realization of multi-input/multi-output (MIMO) switched linear systems (SLSs) from Markov parameters. In the first stage, a linear time-varying (LTV) realization that is topologically…
How can complexity theory and algorithms benefit from practical advances in computing? We give a short overview of some prior work using practical computing to attack problems in computational complexity and algorithms, informally describe…
We introduce a hierarchy of linear systems for showing that a given subspace of pure quantum states is entangled (i.e., contains no product states). This hierarchy outperforms known methods already at the first level, and it is complete in…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
We revisit completion modulo equational theories for left-linear term rewrite systems where unification modulo the theory is avoided and the normal rewrite relation can be used in order to decide validity questions. To that end, we give a…
We formally verify an algorithm for approximate policy iteration on Factored Markov Decision Processes using the interactive theorem prover Isabelle/HOL. Next, we show how the formalized algorithm can be refined to an executable, verified…
This paper considers the use of singular perturbation approximations for a class of linear quantum systems arising in the area of linear quantum optics. The paper presents results on the physical realizability properties of the approximate…